1\name{moranI} 2 3\alias{moranI} 4 5\title{Moran's I Autocorrelation Statistic} 6 7 8\description{ 9Moran's I statistic measures autocorrelation between areas within 10a region. It is similar to the correlation coefficient: 11 12\deqn{ 13I=\frac{n\sum_i\sum_j W_{ij}(Z_i-\overline{Z})(Z_j-\overline{Z})}{2(\sum_i\sum_jW_{ij})\sum_k (Z_k-\overline{Z})^2} 14}{ 15I= n * [sum_i ( sum_j W_ij(Z_i-mean(Z))*(Z_j-mean(Z))]/[2 * (sum_i sum_j W_ij) * sum_k (Z_k-mean(Z))^2] 16} 17 18\eqn{W}{W} is a squared matrix which represents the relationship between each 19pair of regions. An usual approach is set \eqn{w_{ij}}{w_ij} to 1 if regions 20\eqn{i}{i} and \eqn{j}{j} have a common boundary and 0 otherwise, or it may 21represent the inverse distance between the centroids of these two regions. 22 23High values of this statistic may indicate the presence of groups of zones 24where values are unusually high. On the other hand, low values 25of the Moran's statistic will indicate no correlation between neighbouring 26areas, which may lead to indipendance in the observations. 27 28 29\emph{moranI.stat} is the function to calculate the value of the statistic for 30residuals or SMRs of the data. 31 32\emph{moranI.boot} is used when performing a non-parametric bootstrap. 33 34\emph{moranI.pboot} is used when performing a parametric bootstrap. 35} 36 37 38\seealso{ 39DCluster, moranI.stat, moranI.boot, moranI.pboot 40} 41 42\references{ 43Moran, P. A. P. (1948). The interpretation os statistical maps. Journal of the Royal Statistical Society, Series B 10, 243-251. 44} 45 46\keyword{spatial} 47